Optimization of track clustering for primary vertex reconstruction in proton-proton collisions recorded by the CMS experiment at the LHC

Primary-vertex (PV) reconstruction is one of the most computing-intensive stages of the CMS offline workflow and will become a major bottleneck under the increased pile-up foreseen for the High-Luminosity LHC. This thesis introduces CascadeDA, a hybrid vertexing algorithm that combines inexpensive block-wise pre-clustering with a global deterministic-annealing (DA) refinement. Comprehensive benchmarks on high-pile-up Monte-Carlo data show that CascadeDA cuts the mean per-event clustering time from 0.76 s to 0.30 s-an average speed-up of 60 %-while preserving the sub-10 µm z-resolution, > 99 % track-to-vertex assignment efficiency and low fake-fraction of full DA. A systematic scan of block size, block overlap and initial stopping temperature establishes speed–accuracy trade-offs. Compared with the state-of-the-art block algorithm deterministic annealing in blocks (DAB), CascadeDA achieves up to a three-fold reduction in fake vertices and higher robustness in dense pile-up environments. A prototype implementation, in the alpaka accelerator framework, demonstrates architectural portability; although currently CPU-bound and constrained by a hard-coded 0.5 block overlap, it already delivers encouraging vertex-finding efficiency and provides a clear migration path to a fully GPU-resident version. The thesis concludes with a road map towards production deployment-including CUDA enablement, lighter first-loop clusterizers and end-to-end integration into CMS reconstruction, highlighting CascadeDA as a scalable and accurate solution for PV reconstruction at the HL-LHC.